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Optical Aberration Coefficients. XII. Remarks Relating to Aberrations of any Order

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Abstract

This paper concerns itself with certain general details of the “Lagrangian” theory of aberration coefficients previously developed by the author. They are: (i) the general relation between various types of contributions by spherical and aspherical surfaces; (ii) a property of the iteration formulas of any order when the surface is spherical; (iii) the “Principle of Duality” and some of its applications, in particular to the problem of computing a set of coefficients and their duals by means of a single program; (iv) equations for the intrinsic coefficients of spherical aberration of any order when the surface is spherical, and for a related set of coefficients (these being required for an application of the principle of duality); and (v) the groups of identities between aberration coefficients of any order.

© 1965 Optical Society of America

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